Join-Blank代数上的线性系
Linear Systems over Join-Blank Algebras
摘要：
线性代数的一个中心问题是求解线性系。将线性系看作一般半环（V，o次，o+，0，1）上的方程而不是环或域，使得传统的方法无法实现。早期的工作表明，线性系Av = w的解空间X（A;w）在半环类上称为并空白代数，是一个闭区间（在产品顺序）与一个共同的终点的联合。在更小的一类极大空白代数中，1x 1系统Av = w的解空间是闭区间的附加假设意味着X（A;w）是闭区间的有限并。我们检查一般情况下，证明没有这个额外的假设，我们仍然可以使X（A;w）成为一个有限的联盟的准区间。
英文摘要：
A central problem of linear algebra is solving linear systems. Regarding linear systems as equations over general semirings (V,otimes,oplus,0,1) instead of rings or fields makes traditional approaches impossible. Earlier work shows that the solution space X(A;w) of the linear system Av = w over the class of semirings called join-blank algebras is a union of closed intervals (in the product order) with a common terminal point. In the smaller class of max-blank algebras, the additional hypothesis that the solution spaces of the 1x1 systems Av = w are closed intervals implies that X(A;w) is a finite union of closed intervals. We examine the general case, proving that without this additional hypothesis, we can still make X(A;w) into a finite union of quasi-intervals.
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